There are a number of problems with communication systems. The major challenge in signal recovery in mobile communications is to mitigate the inter-symbol-interference effect due to multi-paths and unknown channel fading and distortion. In many communication systems, receivers observe the sum of multiple transmitted signals due to multi-paths, plus any noise. In addition, as a mobile transmitter proceeds along its route, the communication environment is constantly changing. That results in displaced received signals with respect to time and space. Therefore, many wireless communication systems operate under highly dynamic conditions due to the mobility of the mobile unit, varying environmental conditions, and the random nature of channel access. Detecting signals in a receiver encounters many difficulties.
For example, in wireless communication systems, mobile transmitters send symbols at a high data rate. Multiple copies of the signal with delays can interfere with the main signal. This is referred to as “delay spread,” and causes inter-symbol interference (ISI). As a result, equalizers with hundreds of taps may be required.
Another major challenge in signal recovery is to deal with the co-channel interference. Multiple-access or multi-user-detection deals with detecting mutually interfering signals. In the multi-user case, receivers at base stations have to detect signals from multiple users from a combined channel. This is referred to as multi-access interference between different users. The superposition of the signals sent by different mobile transmitters occurs unintentionally. When the same frequency band is used simultaneously by multiple transmitters, as in cellular telephony, personal communications services (PCS), digital television (DTV) broadcasting, and wireless local loops (WLL), sometimes, it is necessary to cancel the co-channel interference from the other users in order to recover the signal for each user.
This interference problem assumes more serious proportions in cellular systems. Due to the mobility of the transmitters, signal strength varies. The strength of the signal from a transmitter closer to a base station is stronger than a signal from a transmitter further away. The signals from the closer transmitter can completely overpower the weaker signal. This is the so-called near-far problem.
All of these problems in mobile communication systems add up to a so-called “blind” channel estimation problem.
Blind Channel Estimation & Signal Recovery
FIG. 1 is a model of the “blind” channel problem. A source signal s 101 is transmitted through a channel H 110 subject to the above conditions. This results in an unknown signal y 102 having time and frequency dispersion. Additive noise 120 further complicates the problem, leading to a received signal r 103. In classic channel estimation, both the input and output signals are usually known. However, in blind channel estimation, only the received signal r 103 is available, and therefore, the effects of the channel H 110 and noise can only be blindly estimated and recovered.
Diversity Combining
Static Combiners
Therefore, it is practical to formulate the signal recovery process as a diversity combiner problem. When channels are non-time-varying, static combiners can be very effective. Static diversity techniques can combat fading channels, because the probability of simultaneous deep fading on all sub-channels is small.
In static diversity combining, a receiver is connected to multiple physically separated antennas. The receiver combines the received signals from each of the antennas. Because the antennas are in space separated, the signal strength in each antenna is independent. Thus, when there is deep fading for one antenna, another antennas probably has a relatively strong signal.
Many types of diversity combining methods are known, see Lee “Communication Design Fundamentals,” Wiley, pp. 116–132, 1993. In a typical mobile communication system, antenna diversity is employed by providing base stations with multiple antennas. The signals received at the antennas are typically combined using maximum ratio combining (MRC). Currently, MRC is the preferred combining technique.
In MRC, the received signals are combined based on the assumption that the interference closely approximates white Gaussian noise. An exemplary MRC scheme is shown in FIG. 2. Each of the signals r1, r2, r3 received at antennas 201–203 in the sub-channels is weighted proportional to the signal-to-noise ratio by selected weighting factors α1, α2, and α3 211–213. The weighted signals 221–223 are combined 230. MRC does not consider correlation between received signals. Therefore, the received signals are detected and equalized individually, and combined by summing.
Dynamic Diversity Combining
However, when channels are dispersive and time varying, it is necessary to resort to a dynamic combining technique. In the prior art, blind single-input-multiple-output (SIMO) equalization, identification, and signal recovery have been used, see for example, Tong et al., “Multichannel Blind Identification: From Subspace to Maximum Likelihood Methods,” Proc. of IEEE, Vol. 86, No. 10, Oct. 1998, and Giannakis et al., “Signal processing advances in wireless and mobile communications,” Vol. 1 & 2, Prentice-Hall, 2001. Those all share the same basic theories and principles of exploiting inherent properties in transmission channel, e.g., constant modulus, cyclostationarity, higher-order statistics, and a slow time-varying source signal, that is, a finite alphabet.
Finite Alphabet Exclusiveness (FAE) Property
The finite alphabet exclusiveness property states that for a given polynomial {tilde over (ƒ)} (D), then {tilde over (ƒ)} (D) {tilde over (s)} (D) is a valid symbol sequence for any arbitrary symbol sequence {tilde over (s)} (D), if and only if {tilde over (ƒ)} (D) is a pure delay, i.e., the overall transfer function {tilde over (ƒ)} (D)=Dk that models the combined delay of the h-domain of the channel and the g-domain of the receiver. This is called the FAE because it is impossible to produce a different valid symbol sequence by any FIR filter under a condition of “excitation” input.
Maximum Likelihood in the H-Domain
Maximum likelihood (ML) methods have frequently been used for estimating FIR parameters. For a general ML formulation, see e.g., Porat “Digital Processing of Random Signals,” Prentice-Hall, 1993. Prior art DML methods focus on the channel side h-domain 220. An unknown parameter h and an input sequence s are determined so as to maximize a density function:{h*,s*}=arg max f(x|h,s).
For a finite alphabet input, a class of iterative ML algorithms was described by Seshadri, “Joint data and channel estimation using blind trellis search techniques,” Proceedings, Globecom'90, pp. 1659–1663, 1991, Ghosh et al. “Maximum likelihood blind equalization,” Opt. Eng., Vol.31, No. 6, pp. 1224–1228, June 1992, U.S. Pat. No. 5,208,816 “Generalized Viterbi decoding algorithms,” issued to Seshardi, et al. May 4, 1993, and U.S. Pat. No. 5,406,585 “Method and apparatus for trellis decoding in a multiple-access system,” issued to Rohani, et al. on Apr. 11, 1995.
At an iteration j, with a guess of the initial input sequence s(j), the channel h(j) was estimated by solving the following least-square formulation:h(j)=arg minh∥x−s(j)*h(j)∥.
In the same iteration j, with the new channel estimate h(j), a new input sequence, denoted as s(j+1), will be estimated by:s(j+1)=arg minss∥x−s(j+1)*h(j)∥,where, ss stood for the valid symbol set. This step required a probability lattice and a Viterbi search, which are known to be computationally expensive.
Tong et al. used a deconvolutional approach, where an inverse system is represented by an IIR filter. The blind deconvolution approach is used for many applications, especially when the number of outputs equals the inputs, specifically a single input, single output (SISO) system. Giannakis et al. used a convolutional approach, where the inverse system is represented by several FIR filters. The convolutional approach, via FIR filters, offer an attractive alternative when the number of output signals exceeds the number of that of the input signals.
Therefore, there is a need for a dynamic diversity combiner that can recover signals in channels subject to multi-access interference, multi-path fading, varying power levels of transmitters, and noise. Furthermore, it is desired to recover the signals without having to determine channel parameters using resource consuming probabilistic lattices and time consuming searches.